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Weighted Generalized Hardy Inequalities for Nonincreasing Functions

Published online by Cambridge University Press:  20 November 2018

Kenneth F. Andersen
Kenneth F. Andersen*
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1
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Abstract

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The nonnegative weight function pairs u, v for which the operator maps the nonnegative nonincreasing functions in LP(v) boundedly into weak Lq(u) are characterized. This result is used, in particular, both to generalize and to provide an alternate proof of certain strong type inequalities recently obtained by Ariño and Muckenhouptfor the Hardy averaging operator restricted to nonnegative nonincreasing functions.

Keywords

26D1542B25Weighted inequalitiesweak type inequalityHardy's inequality
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1121 - 1135
Copyright
Copyright © Canadian Mathematical Society 1991

References

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